Formal Gevrey solutions: in analytic germs - for higher order holomorphic PDEs
Identifiers
Permanent link (URI): http://hdl.handle.net/10017/55197DOI: 10.1007/s00208-022-02393-w
ISSN: 0025-5831
Publisher
Springer
Date
2022-04-02Funders
Agencia Estatal de Investigación
Universidad de Alcalá
Bibliographic citation
Carrillo, S.A. & Lastra, A. 2022, "Formal Gevrey solutions: in analytic germs - for higher order holomorphic PDEs", Mathematische Annalen (2022).
Project
info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019-105621GB-I00/ES/METODOS ASINTOTICOS, ALGEBRAICOS Y GEOMETRICOS EN FOLIACIONES SINGULARES Y SISTEMAS DINAMICOS/
info:eu-repo/grantAgreement/UAH//CM-JIN-2019-010
Document type
info:eu-repo/semantics/article
Version
info:eu-repo/semantics/publishedVersion
Publisher's version
https://doi.org/10.1007/s00208-022-02393-wRights
Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
Access rights
info:eu-repo/semantics/openAccess
Abstract
We consider a family of holomorphic PDEs whose singular locus is given by the zero set
of an analytic map P with P(0) = 0. Our goal is to establish conditions for the existence
and uniqueness of formal power series solutions and to determine their divergence rate. In
fact, we prove that the solution is Gevrey in P, giving new information on divergency while
compared to the classical Gevrey classes. If P is not singular at 0, we also provide Poincaré
conditions to recover convergent solutions. Our strategy is to extend the dimension and
lift the given PDE to a problem where results of singular PDEs can be applied. Finally,
examples where the Gevrey class in P is optimal are included.
Files in this item
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Formal_Carrillo_Math_Ann_2022.pdf | 488.4Kb |
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